An insurance company is interested in conducting a study to estimate the population proportion of teenagers who obtain a driving permit within 1 year of their 16^th birthday.A level of confidence of 99% will be used and an error of no more than .04 is desired.There is no knowledge as to what the population proportion will be.The approximate sample size should be at least _______. A)1037 B)160 C)41 D)259 E)289

Question

Quizplus · Accepted Answer

To estimate the minimum sample size needed for a proportion with a specified level of confidence and margin of error when the population proportion is unknown, the formula $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$ is used, where $Z$ is the Z-score corresponding to the desired level of confidence, $p$ is the estimated proportion (0.5 when unknown, as it maximizes the sample size), and $E$ is the margin of error. For a 99% confidence level, the Z-score is approximately 2.576. Substituting $Z = 2.576$, $p = 0.5$, and $E = 0.04$ into the formula gives $n = \frac{(2.576)^2 \cdot 0.5 \cdot (1-0.5)}{(0.04)^2}$, which calculates to approximately 1037.

An Insurance Company Is Interested in Conducting a Study to Estimate